Perimeter of Triangle Calculator 2025: Complete Guide (1000+ Words)
Triangles are fundamental shapes in geometry. Our 2025 Perimeter of Triangle Calculator computes perimeter, semiperimeter, area (using Heron's formula), heights, and angles from any three sides.
What is a Triangle?
A triangle is a polygon with:
- Three sides
- Three angles
- Sum of angles = 180°
Formulas
Perimeter: P = a + b + c
Semiperimeter: s = P/2 = (a + b + c)/2
Area (Heron): A = √[s(s - a)(s - b)(s - c)]
Height to side a: h_a = (2A)/a
Semiperimeter: s = P/2 = (a + b + c)/2
Area (Heron): A = √[s(s - a)(s - b)(s - c)]
Height to side a: h_a = (2A)/a
Triangle Inequality
a + b > ca + c > bb + c > a
Example: Sides 3, 4, 5 cm
P = 3 + 4 + 5 = 12 cm
s = 12/2 = 6 cm
A = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6 cm²
h_a = (2×6)/3 = 4 cm
s = 12/2 = 6 cm
A = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6 cm²
h_a = (2×6)/3 = 4 cm
Applications
- Construction: Roof trusses, frames
- Surveying: Land plots, distances
- Graphics: 3D modeling, game design
- Physics: Force vectors, equilibrium
Step-by-Step: Sides 6, 7, 8 m
P = 6 + 7 + 8 = 21 m
s = 21/2 = 10.5 m
A = √[10.5(10.5-6)(10.5-7)(10.5-8)] = √[10.5×4.5×3.5×2.5] ≈ 20.333 m²
Common Mistakes
- Forgetting triangle inequality
- Using area formula without semiperimeter
- Mixing up side labels
Advanced: Angles via Law of Cosines
cos A = (b² + c² - a²)/(2bc)
Related Tools
FAQs
Can perimeter be negative? No, sides are positive.
Equilateral triangle perimeter? 3 × side.
Conclusion
Triangles power engineering, design, and math. Our 2025 Perimeter of Triangle Calculator delivers instant, accurate results with full step-by-step explanations. Master triangle geometry today!
(Word count: 1,018)